`a,`

Đặt `A = sqrt 2024 - sqrt 2023`

`A(sqrt 2024 + sqrt 2023) = (sqrt 2024 - sqrt 2023) (sqrt 2024 + sqrt 2023)=1`

`A=1/(sqrt 2024 + sqrt 2023)`

Đặt `B=sqrt 2023 - sqrt 2022`

`B(sqrt 2023 + sqrt 2022)=(sqrt 2023 - sqrt 2022)(sqrt 2023 + sqrt 2022) = 1`

`B=1/(sqrt 2023 + sqrt 2022)`

Vì `sqrt 2024 > sqrt 2022` nên `sqrt 2024 + sqrt 2023 > sqrt 2023 + sqrt 2022`

suy ra `1/(sqrt 2023 + sqrt 2023) < 1/(sqrt 2023 + sqrt2022)`

hay `A <B`

Vậy `sqrt 2024 - sqrt 2023 < sqrt 2023 - sqrt 2022`

`b,` 

Đặt `A=sqrt{a+b}`

`A^2 = (sqrt {a+b})^2`

`A^2 = a+b`

Đặt `B = sqrt a + sqrt b`

`B^2 = (sqrt a + sqrt b)^2`

`=a + 2sqrt {ab} + b`

Vì `a>0` và `b>0` nên `2sqrt{ab} >0`

Khi  đó `A^2 < B^2`

Suy ra `A<B`

Vậy `sqrt{a+b} < sqrt a + sqrt b`